Abstract

Disc degeneration, usually associated with low back pain and changes of intervertebral stiffness, represents a major health issue. As the intervertebral disc (IVD) morphology influences its stiffness, the link between mechanical properties and degenerative grade is partially lost without an efficient normalization of the stiffness with respect to the morphology. Moreover, although the behavior of soft tissues is highly nonlinear, only linear normalization protocols have been defined so far for the disc stiffness. Thus, the aim of this work is to propose a nonlinear normalization based on finite elements (FE) simulations and evaluate its impact on the stiffness of human anatomical specimens of lumbar IVD. First, a parameter study involving simulations of biomechanical tests (compression, flexion/extension, bilateral torsion and bending) on 20 FE models of IVDs with various dimensions was carried out to evaluate the effect of the disc's geometry on its compliance and establish stiffness/morphology relations necessary to the nonlinear normalization. The computed stiffness was then normalized by height (H), cross-sectional area (CSA), polar moment of inertia (J) or moments of inertia (Ixx, Iyy) to quantify the effect of both linear and nonlinear normalizations. In the second part of the study, T1-weighted MRI images were acquired to determine H, CSA, J, Ixx and Iyy of 14 human lumbar IVDs. Based on the measured morphology and pre-established relation with stiffness, linear and nonlinear normalization routines were then applied to the compliance of the specimens for each quasi-static biomechanical test. The variability of the stiffness prior to and after normalization was assessed via coefficient of variation (CV). The FE study confirmed that larger and thinner IVDs were stiffer while the normalization strongly attenuated the effect of the disc geometry on its stiffness. Yet, notwithstanding the results of the FE study, the experimental stiffness showed consistently higher CV after normalization. Assuming that geometry and material properties affect the mechanical response, they can also compensate for one another. Therefore, the larger CV after normalization can be interpreted as a strong variability of the material properties, previously hidden by the geometry's own influence. In conclusion, a new normalization protocol for the intervertebral disc stiffness in compression, flexion, extension, bilateral torsion and bending was proposed, with the possible use of MRI and FE to acquire the discs' anatomy and determine the nonlinear relations between stiffness and morphology. Such protocol may be useful to relate the disc's mechanical properties to its degree of degeneration.

Figures

The parameter study involved four sets of five FE models with various dimensions. Compression (C), torsion (right/left), lateral bending (right/left), and flexion (F)/extension (E) were simulated with two different material properties.

An exponential function or a double sigmoid (Exp fit) was fitted to the experimental data (Exp data). Ki, Kf and Kt were computed as the initial slope (NZ stiffness), final slope of the curves and load applied over the deflection. To include even the stiffest discs, Kf and Kt were calculated at 15% strain in compression or a ±3 deg angle for the flexibility tests (here lateral bending). BR: bending right (moment > 0) and BL: bending left (moment < 0).

Variability of the stiffness prior to and after normalization was assessed via CV. CVs of measured (K), linearly normalized (KNormL) and nonlinearly normalized (KNormNL) stiffnesses (Ki, Kf, Kt) are presented for each loadcase (compression, torsion, bending, flexion, extension). “All tests” presents the average CVs of Ki, Kf, and Kt when accounting for all loadcases. “All stiffnesses” presents the average CVs of measured and normalized data for all stiffnesses and loadcases with the associated p values.

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